Wiedemann-Franz Relation and Thermal-Transistor Effect in Suspended Graphene

We extract experimentally the electronic thermal conductivity, K-e, in suspended graphene that we dope using a back-gate electrode. We make use of two-point dc electron transport at low bias voltages and intermediate temperatures (50-160 K), where the electron and lattice temperatures are decoupled. The thermal conductivity is proportional to the charge conductivity times the temperature, confirming that the Wiedemann-Franz relation is obeyed in suspended graphene. We extract an estimate of the Lorenz coefficient as 1.1-1.7 x 10(-8) W Omega K-2. K-e shows a transistor effect and can be tuned with the back-gate by more than a factor of 2 as the charge carrier density ranges from similar to 0.5 to 1.8 x 10(11) cm(-2).